Demazure Characters and Affine Fusion Rules

Details Demazure Characters and Affine Fusion Rules Demazure Characters and Affine Fusion Rules

1996-12-14

arxiv.org/abs/hep-th/9612159v1

J.Math.Phys. 39 (1998) 665-681

Physics

High Energy Physics

High Energy Physics - Theory

23 pages, TeX, uses harvmac

Scientific paper

10.1063/1.532340

The Demazure character formula is applied to the Verlinde formula for affine fusion rules. We follow Littelmann's derivation of a generalized Littlewood-Richardson rule from Demazure characters. A combinatorial rule for affine fusions does not result, however. Only a modified version of the Littlewood-Richardson rule is obtained that computes an (old) upper bound on the fusion coefficients of affine $A_r$ algebras. We argue that this is because the characters of simple Lie algebras appear in this treatment, instead of the corresponding affine characters. The Bruhat order on the affine Weyl group must be implicated in any combinatorial rule for affine fusions; the Bruhat order on subgroups of this group (such as the finite Weyl group) does not suffice.

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